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  <a class="pure-menu-link nav4" onclick="animateByNav()" href="#_1">机器学习的核心概念</a>
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  <a class="pure-menu-link nav4" onclick="animateByNav()" href="#_2">机器学习方法</a>
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  <a class="pure-menu-link nav5" onclick="animateByNav()" href="#_3">按照学习方式分</a>
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  <a class="pure-menu-link nav5" onclick="animateByNav()" href="#_4">按照<strong>学习任务</strong>分</a>
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  <a class="pure-menu-link nav4" onclick="animateByNav()" href="#_5">机器学习工具</a>
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  <a class="pure-menu-link nav4" onclick="animateByNav()" href="#_6">各种神经网络</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#1-1">1-1. 欢迎参加《机器学习》课程</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#1-2">1-2. 什么是机器学习？</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#1-3">1-3. 监督学习</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#1-4">1-4. 无监督学习</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#2-1">2-1. 模型描述</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#2-2">2-2. 代价函数</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#2-3">2-3. 代价函数（一）</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#2-4">2-4. 代价函数（二）</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#2-5">2-5. 梯度下降</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#2-6">2-6. 梯度下降知识点总结</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#2-7">2-7. 线性回归的梯度下降</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#3-1">3-1. 矩阵和向量</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#3-2">3-2. 加法和标量乘法</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#3-3">3-3. 矩阵向量乘法</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#3-4">3-4. 矩阵乘法</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#3-5">3-5. 矩阵乘法特征</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#3-6">3-6. 逆和转置</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#4-1">4-1. 多功能</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#4-2">4-2. 多元梯度下降法</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#4-3">4-3. 多元梯度下降法演练：特征缩放</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#4-4-ii">4-4. 多元梯度下降法II：学习率</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#4-5">4-5. 特征和多项式回归</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#4-6">4-6. 正规方程（区别于迭代方法的直接解法）</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#4-7">4-7. 正规方程在矩阵不可逆情况下的解决方法</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#4-8">4-8. 导师的编程小技巧</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#5-1">5-1. 基本操作</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#5-2">5-2. 移动数据</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#5-3">5-3. 计算数据</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#5-4">5-4. 数据绘制</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#5-5-forwhileif">5-5. 控制语句：for，while，if</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#5-6">5-6. 矢量</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#6-1">6-1. 分类</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#6-2">6-2. 假设陈述</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#6-3">6-3. 决策界限</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#6-4">6-4. 代价函数</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#6-5">6-5. 简化代价函数与梯度下降</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#6-6">6-6. 高级优化</a>
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  <a class="pure-menu-link nav4" onclick="animateByNav()" href="#gradient-descent">Gradient descent 梯度下降法</a>
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  <a class="pure-menu-link nav4" onclick="animateByNav()" href="#conjugate-gradient">Conjugate gradient 共轭梯度法</a>
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  <a class="pure-menu-link nav4" onclick="animateByNav()" href="#bfgs">BFGS</a>
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  <a class="pure-menu-link nav4" onclick="animateByNav()" href="#l-bfgs">L-BFGS</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#6-7">6-7. 多元分类：一对多</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#7-1">7-1. 过拟合问题</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#7-2">7-2. 代价函数</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#7-3">7-3. 线性回归的正则化</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#7-4">7-4. 逻辑回归的正则化</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#8-1">8-1. 非线性假设</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#8-2">8-2. 神经元与大脑</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#8-3-i">8-3. 模型展示Ⅰ</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#8-4-ii">8-4. 模型展示Ⅱ</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#8-5-i">8-5. 例子与直觉理解Ⅰ</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#8-6-ii">8-6. 例子与直觉理解Ⅱ</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#8-7">8-7. 多元分类</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#9-1">9-1. 代价函数</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#9-2">9-2. 反向传播算法</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#9-3">9-3. 理解反向传播</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#9-4">9-4. 使用注意：展开参数</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#9-5">9-5. 梯度检测</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#9-6">9-6. 随机初始化</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#9-7">9-7. 组合到一起</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#9-8">9-8. 无人驾驶</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#10-1">10-1. 决定下一步做什么</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#10-2">10-2. 评估假设</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#10-3">10-3. 模型选择和训练、验证、测试集</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#10-4">10-4. 诊断偏差与方差</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#10-5">10-5. 正则化和偏差、方差</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#10-6">10-6. 学习曲线</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#10-7">10-7. 决定接下来做什么</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#11-1">11-1. 确定执行的优先级</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#11-2">11-2. 误差分析</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#11-3">11-3. 不对称性分类的误差评估</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#11-4">11-4. 精确度和召回率的权衡</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#11-5">11-5. 机器学习数据</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#12-1">12-1. 优化目标</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#12-2">12-2. 直观上对大间隔的理解</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#12-3">12-3. 大间隔分类器的数学原理</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#12-4-1">12-4. 核函数1</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#12-5-2">12-5. 核函数2</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#12-6-svm">12-6. 使用SVM</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#13-1">13-1. 无监督学习</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#13-2-k-means">13-2. K-Means算法</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#13-3">13-3. 优化目标</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#13-4">13-4. 随机初始化</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#13-5">13-5. 选取聚类数量</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#14-1-i">14-1. 目标. I：数据压缩</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#14-2-ii">14-2. 目标. II：可视化</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#14-3-1">14-3. 主成分分析问题规划1</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#14-4-2">14-4. 主成分分析问题规划2</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#14-5">14-5. 主成分数量选择</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#14-6">14-6. 压缩重现</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#14-7-pca">14-7. 应用. PCA. 的建议</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#15-1">15-1. 问题动机</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#15-2">15-2. 高斯分布</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#15-3">15-3. 算法</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#15-4">15-4. 开发和评估异常检测系统</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#15-5-vs">15-5. 异常检测. VS. 监督学习</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#15-6">15-6. 选择要使用的功能</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#15-7">15-7. 多变量高斯分布</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#15-8">15-8. 使用多变量高斯分布的异常检测</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#16-1">16-1. 问题规划</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#16-2">16-2. 基于内容的推荐算法</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#16-3">16-3. 协同过滤</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#16-4">16-4. 协同过滤算法</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#16-5">16-5. 矢量化：低轶矩阵分解</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#16-6">16-6. 实施细节：均值规范化</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#17-1">17-1. 学习大数据集</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#17-2">17-2. 随机梯度下降</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#17-3-mini-batch">17-3. Mini-Batch. 梯度下降</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#17-4">17-4. 随机梯度下降收敛</a>
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<li class="pure-menu-item">
  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#17-5">17-5. 在线学习</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#17-6">17-6. 减少映射与数据并行</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#18-1-ocr-pipeline">18-1. 问题描述与. OCR. pipeline</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#18-2">18-2. 滑动窗口</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#18-3">18-3. 获取大量数据和人工数据</a>
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  <a class="pure-menu-link nav2" onclick="animateByNav()" href="#19-1">19-1. 总结与感谢</a>
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<div id="content-articles">
  <h1 id="吴恩达机器学习" class="content-subhead">吴恩达机器学习</h1>
  <p>
    <span>2021-01-14</span>
    <span><span class="post-category post-category-machine-learning">Machine Learning</span></span>
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  <div id="content-articles-markdown">
    <h4 id="_1">机器学习的核心概念</h4>
<p>第一类，预测学习。</p>
<p>第二类，特征设计。</p>
<p>第三类，函数逼近。</p>
<p>第四类，数值优化。</p>
<h4 id="_2">机器学习方法</h4>
<h5 id="_3">按照学习方式分</h5>
<div class="pure-table-scrollable"><table class="pure-table pure-table-horizontal">
<thead>
<tr>
<th align="left">学习方式</th>
<th align="left">英文</th>
<th align="left">描述</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">监督式学习</td>
<td align="left">Supervised Learning</td>
<td align="left">训练集对象：有标注；如回归分析，统计分类</td>
</tr>
<tr>
<td align="left">非监督式学习</td>
<td align="left">Unsupervised Leanring</td>
<td align="left">训练集对象：无标注；如聚类、GAN(生成对抗网络)</td>
</tr>
<tr>
<td align="left">半监督式学习</td>
<td align="left">Semi-supervised Leanring</td>
<td align="left">介于监督式与无监督式之间</td>
</tr>
<tr>
<td align="left">增强学习</td>
<td align="left">Reinforcement Leanring</td>
<td align="left">智能体不断与环境进行交互，通过试错的方式来获得最佳策略</td>
</tr>
</tbody>
</table></div>
<h5 id="_4">按照<strong>学习任务</strong>分</h5>
<div class="pure-table-scrollable"><table class="pure-table pure-table-horizontal">
<thead>
<tr>
<th align="left">学习任务</th>
<th align="left">英文</th>
<th align="left">描述</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">回归</td>
<td align="left">Regression</td>
<td align="left">回归是预测一个数量 （是连续的），属于监督学习</td>
</tr>
<tr>
<td align="left">分类</td>
<td align="left">Classification</td>
<td align="left">分类是预测一个标签 （是离散的），属于监督学习</td>
</tr>
<tr>
<td align="left">聚类</td>
<td align="left">Clustering</td>
<td align="left">属于无监督学习</td>
</tr>
</tbody>
</table></div>
<h4 id="_5">机器学习工具</h4>
<p>GoogLeNet</p>
<p>AlexNet</p>
<p>Kaggle</p>
<p>Colab</p>
<h4 id="_6">各种神经网络</h4>
<div class="pure-table-scrollable"><table class="pure-table pure-table-horizontal">
<thead>
<tr>
<th></th>
<th></th>
<th></th>
</tr>
</thead>
<tbody>
<tr>
<td>前馈神经网络</td>
<td>FNN</td>
<td>人工智能领域中最早发明的简单人工神经网络类型。在它内部，参数从输入层经过隐含层向输出层单向传播。与递归神经网络不同，在它内部不会构成有向环。</td>
</tr>
<tr>
<td>反向传播神经网络</td>
<td>BP</td>
<td></td>
</tr>
<tr>
<td>深度神经网络</td>
<td>DNN</td>
<td></td>
</tr>
<tr>
<td>卷积神经网络</td>
<td>CNN</td>
<td></td>
</tr>
<tr>
<td>K最邻近</td>
<td>KNN</td>
<td></td>
</tr>
<tr>
<td>多层感知机</td>
<td>MLP</td>
<td></td>
</tr>
<tr>
<td>支持向量机</td>
<td>SVN</td>
<td></td>
</tr>
</tbody>
</table></div>
<h2 id="1-1">1-1. 欢迎参加《机器学习》课程</h2>
<h2 id="1-2">1-2. 什么是机器学习？</h2>
<h2 id="1-3">1-3. 监督学习</h2>
<h2 id="1-4">1-4. 无监督学习</h2>
<h2 id="2-1">2-1. 模型描述</h2>
<h2 id="2-2">2-2. 代价函数</h2>
<h2 id="2-3">2-3. 代价函数（一）</h2>
<h2 id="2-4">2-4. 代价函数（二）</h2>
<h2 id="2-5">2-5. 梯度下降</h2>
<h2 id="2-6">2-6. 梯度下降知识点总结</h2>
<h2 id="2-7">2-7. 线性回归的梯度下降</h2>
<h2 id="3-1">3-1. 矩阵和向量</h2>
<h2 id="3-2">3-2. 加法和标量乘法</h2>
<h2 id="3-3">3-3. 矩阵向量乘法</h2>
<h2 id="3-4">3-4. 矩阵乘法</h2>
<h2 id="3-5">3-5. 矩阵乘法特征</h2>
<h2 id="3-6">3-6. 逆和转置</h2>
<h2 id="4-1">4-1. 多功能</h2>
<h2 id="4-2">4-2. 多元梯度下降法</h2>
<h2 id="4-3">4-3. 多元梯度下降法演练：特征缩放</h2>
<h2 id="4-4-ii">4-4. 多元梯度下降法II：学习率</h2>
<h2 id="4-5">4-5. 特征和多项式回归</h2>
<h2 id="4-6">4-6. 正规方程（区别于迭代方法的直接解法）</h2>
<h2 id="4-7">4-7. 正规方程在矩阵不可逆情况下的解决方法</h2>
<h2 id="4-8">4-8. 导师的编程小技巧</h2>
<h2 id="5-1">5-1. 基本操作</h2>
<h2 id="5-2">5-2. 移动数据</h2>
<h2 id="5-3">5-3. 计算数据</h2>
<h2 id="5-4">5-4. 数据绘制</h2>
<h2 id="5-5-forwhileif">5-5. 控制语句：for，while，if</h2>
<h2 id="5-6">5-6. 矢量</h2>
<h2 id="6-1">6-1. 分类</h2>
<h2 id="6-2">6-2. 假设陈述</h2>
<h2 id="6-3">6-3. 决策界限</h2>
<h2 id="6-4">6-4. 代价函数</h2>
<h2 id="6-5">6-5. 简化代价函数与梯度下降</h2>
<h2 id="6-6">6-6. 高级优化</h2>
<h4 id="gradient-descent">Gradient descent 梯度下降法</h4>
<h4 id="conjugate-gradient">Conjugate gradient 共轭梯度法</h4>
<h4 id="bfgs">BFGS</h4>
<h4 id="l-bfgs">L-BFGS</h4>
<p>在 Octave 上求最小化代价函数</p>
<pre><code class="pre-wrap"><span style="overflow-x: auto; max-width:100%; display:inline;"><code class="language-octave">function [jVal, gradient] = costFunction(theta)
    jVal = (theta(1)-5)^2+(theta(2)-5)^2;
    gradient = zeros(2,1);
    gradient(1) = 2*(theta(1)-5);
    gradient(2) = 2*(theta(2)-5);
end

options = optimset('GradObj','on','MaxIter','100');
initialTheta = zeros(2,1);

[optTheta, functionVal, exitFlag] = fminunc(@costFunction, initialTheta, options);
</code></span></code></pre>
<h2 id="6-7">6-7. 多元分类：一对多</h2>
<p><img class="pure-img" src="https://zromyk.gitee.io/myblog-figurebed/post/吴恩达机器学习.assets/20213182120.jpg" alt="2021318212021321" style="zoom:50%;" /></p>
<h2 id="7-1">7-1. 过拟合问题</h2>
<p><img class="pure-img" src="https://zromyk.gitee.io/myblog-figurebed/post/吴恩达机器学习.assets/20210318212247.jpg" alt="20210318212247" style="zoom:50%;" /></p>
<p><img class="pure-img" src="https://zromyk.gitee.io/myblog-figurebed/post/吴恩达机器学习.assets/20210318212450.jpg" alt="20210318212450" style="zoom:50%;" /></p>
<h2 id="7-2">7-2. 代价函数</h2>
<h2 id="7-3">7-3. 线性回归的正则化</h2>
<p>在代价函数中加入惩罚项防止过拟合：<br />
<script type="math/tex; mode=display">
J(\theta)=\cfrac{1}{2m}[\sum_{i=1}^m(h_\theta(\pmb{x}^{(i)})-y^{(i)})^2+\lambda\sum_{j=1}^n\theta_j^2] \\
</script>
<br />
加入正则项：<br />
<script type="math/tex; mode=display">
\begin{equation}\begin{split} 
\theta_0 &= \theta_0-\alpha\frac{1}{m}\sum_{i=1}^m(h_\theta(\pmb{x}^{(i)})-y^{(i)})\pmb{x}_0^{(i)} \\
\theta_j &= \theta_j-\alpha[\frac{1}{m}\sum_{i=1}^m(h_\theta(\pmb{x}^{(i)})-y^{(i)})\pmb{x}_j^{(i)}+\lambda\cfrac{1}{m}\theta_j]
\end{split}\end{equation}
</script>
<br />
即：<br />
<script type="math/tex; mode=display">
\theta_j = \theta_j(1-\alpha\lambda\cfrac{1}{m})-\alpha\frac{1}{m}\sum_{i=1}^m(h_\theta(\pmb{x}^{(i)})-y^{(i)})\pmb{x}_j^{(i)}\\
</script>
</p>
<h2 id="7-4">7-4. 逻辑回归的正则化</h2>
<p>在代价函数中加入惩罚项防止过拟合：<br />
<script type="math/tex; mode=display">
J(\theta)=-\cfrac{1}{m}\sum_{i=1}^m[y^{(i)}\log{h_\theta(\pmb{x}^{(i)})}+(1-y^{(i)})\log{(1-h_\theta(\pmb{x}^{(i)}))}] + \lambda\cfrac{1}{2m}\sum_{j=1}^n\theta_j^2 \\
</script>
<br />
加入正则项：<br />
<script type="math/tex; mode=display">
\begin{equation}\begin{split} 
\theta_0 &= \theta_0-\alpha\frac{1}{m}\sum_{i=1}^m(h_\theta(\pmb{x}^{(i)})-y^{(i)})\pmb{x}_0^{(i)} \\
\theta_j &= \theta_j-\alpha[\frac{1}{m}\sum_{i=1}^m(h_\theta(\pmb{x}^{(i)})-y^{(i)})\pmb{x}_j^{(i)}+\lambda\cfrac{1}{m}\theta_j] \\
\end{split}\end{equation}
</script>
<br />
即：<br />
<script type="math/tex; mode=display">
\theta_j = \theta_j(1-\alpha\lambda\cfrac{1}{m})-\alpha\frac{1}{m}\sum_{i=1}^m(h_\theta(\pmb{x}^{(i)})-y^{(i)})\pmb{x}_j^{(i)}\\
</script>
<br />
其中：<br />
<script type="math/tex; mode=display">
h_0(\pmb{x}^{(i)}) = \cfrac{1}{1+e^{-\pmb{\theta}^T\pmb{x}^{(i)}}}
</script>
</p>
<h2 id="8-1">8-1. 非线性假设</h2>
<h2 id="8-2">8-2. 神经元与大脑</h2>
<h2 id="8-3-i">8-3. 模型展示Ⅰ</h2>
<h2 id="8-4-ii">8-4. 模型展示Ⅱ</h2>
<h2 id="8-5-i">8-5. 例子与直觉理解Ⅰ</h2>
<h2 id="8-6-ii">8-6. 例子与直觉理解Ⅱ</h2>
<h2 id="8-7">8-7. 多元分类</h2>
<h2 id="9-1">9-1. 代价函数</h2>
<h2 id="9-2">9-2. 反向传播算法</h2>
<h2 id="9-3">9-3. 理解反向传播</h2>
<h2 id="9-4">9-4. 使用注意：展开参数</h2>
<h2 id="9-5">9-5. 梯度检测</h2>
<h2 id="9-6">9-6. 随机初始化</h2>
<h2 id="9-7">9-7. 组合到一起</h2>
<h2 id="9-8">9-8. 无人驾驶</h2>
<h2 id="10-1">10-1. 决定下一步做什么</h2>
<h2 id="10-2">10-2. 评估假设</h2>
<h2 id="10-3">10-3. 模型选择和训练、验证、测试集</h2>
<h2 id="10-4">10-4. 诊断偏差与方差</h2>
<h2 id="10-5">10-5. 正则化和偏差、方差</h2>
<h2 id="10-6">10-6. 学习曲线</h2>
<h2 id="10-7">10-7. 决定接下来做什么</h2>
<h2 id="11-1">11-1. 确定执行的优先级</h2>
<h2 id="11-2">11-2. 误差分析</h2>
<h2 id="11-3">11-3. 不对称性分类的误差评估</h2>
<h2 id="11-4">11-4. 精确度和召回率的权衡</h2>
<h2 id="11-5">11-5. 机器学习数据</h2>
<h2 id="12-1">12-1. 优化目标</h2>
<h2 id="12-2">12-2. 直观上对大间隔的理解</h2>
<h2 id="12-3">12-3. 大间隔分类器的数学原理</h2>
<h2 id="12-4-1">12-4. 核函数1</h2>
<h2 id="12-5-2">12-5. 核函数2</h2>
<h2 id="12-6-svm">12-6. 使用SVM</h2>
<h2 id="13-1">13-1. 无监督学习</h2>
<h2 id="13-2-k-means">13-2. K-Means算法</h2>
<h2 id="13-3">13-3. 优化目标</h2>
<h2 id="13-4">13-4. 随机初始化</h2>
<h2 id="13-5">13-5. 选取聚类数量</h2>
<h2 id="14-1-i">14-1. 目标. I：数据压缩</h2>
<h2 id="14-2-ii">14-2. 目标. II：可视化</h2>
<h2 id="14-3-1">14-3. 主成分分析问题规划1</h2>
<h2 id="14-4-2">14-4. 主成分分析问题规划2</h2>
<h2 id="14-5">14-5. 主成分数量选择</h2>
<h2 id="14-6">14-6. 压缩重现</h2>
<h2 id="14-7-pca">14-7. 应用. PCA. 的建议</h2>
<h2 id="15-1">15-1. 问题动机</h2>
<h2 id="15-2">15-2. 高斯分布</h2>
<h2 id="15-3">15-3. 算法</h2>
<h2 id="15-4">15-4. 开发和评估异常检测系统</h2>
<h2 id="15-5-vs">15-5. 异常检测. VS. 监督学习</h2>
<h2 id="15-6">15-6. 选择要使用的功能</h2>
<h2 id="15-7">15-7. 多变量高斯分布</h2>
<h2 id="15-8">15-8. 使用多变量高斯分布的异常检测</h2>
<h2 id="16-1">16-1. 问题规划</h2>
<h2 id="16-2">16-2. 基于内容的推荐算法</h2>
<h2 id="16-3">16-3. 协同过滤</h2>
<h2 id="16-4">16-4. 协同过滤算法</h2>
<h2 id="16-5">16-5. 矢量化：低轶矩阵分解</h2>
<h2 id="16-6">16-6. 实施细节：均值规范化</h2>
<h2 id="17-1">17-1. 学习大数据集</h2>
<h2 id="17-2">17-2. 随机梯度下降</h2>
<h2 id="17-3-mini-batch">17-3. Mini-Batch. 梯度下降</h2>
<h2 id="17-4">17-4. 随机梯度下降收敛</h2>
<h2 id="17-5">17-5. 在线学习</h2>
<h2 id="17-6">17-6. 减少映射与数据并行</h2>
<h2 id="18-1-ocr-pipeline">18-1. 问题描述与. OCR. pipeline</h2>
<h2 id="18-2">18-2. 滑动窗口</h2>
<h2 id="18-3">18-3. 获取大量数据和人工数据</h2>
<h2 id="18-4-pipeline">18-4. 天花板分析：下一步工作的 pipeline</h2>
<h2 id="19-1">19-1. 总结与感谢</h2>
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  };
</script>

</body>
</html>
